A major third is 2^(4/12) -> 1.2599, which is clearly closest to 5/4. Why the hell would you round that all the way up to 9/7 for a more dissonant chord that's almost closer to the next half-step up anyway? The whole point of a major interval is to sound bright and happy.

A major third is 2^(4/12) -> 1.2599, which is clearly closest to 5/4. Why the hell would you round that all the way up to 9/7 for a more dissonant chord that's almost closer to the next half-step up anyway? The whole point of a major interval is to sound bright and happy.

You take your quarter-tone bullshit and get out, sir.

Being 13.7 cents off 5/4 puts the 12-EDO major third closer to the significantly more dissonant Pythagorean 81/64 third - or, if we are to be generous, to 24/19, which is *technically* a just interval but is still far more complex than 9/7, which makes a great bright upward-leading third within a chord (9/7 to 4/3 is very dramatic) in addition to just sounding different and cool. (Furthermore, superpyth tunings by and large have much more accurate versions of 5/4 than 12-EDO does, albeit as an "augmented second.")

Also the simplest typical superpyth is a twelve-note subset of 22-EDO, the basic diatonic "semitone" of which is very close to a quartertone as conventionally understood, but the cumulative effect is quite different.

Probably either the Hendrix chord or the Battaglia chord. I considered saying the Cuthbert triad but that doesn't really exist in 22-EDO (or really most basic superpyth scales), although it does exist in a whole slew of other tunings with supermajor chords.